arXiv:2303.06985 · Proceedings of the National Academy of Sciences
Fermionic quantum processing with programmable neutral atom arrays
Daniel González-Cuadra, Dolev Bluvstein, M. Kalinowski, Raphael Kaubruegger, Nishad Maskara, Piero Naldesi, Torsten V. Zache, Adam M. Kaufman, Mikhail D. Lukin, Hannes Pichler, Benoît Vermersch, Jun Ye, P. Zoller
Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics.-5.4pc]Please note that the spelling of the following author names in the manuscript differs from the spelling provided in the article metadata: D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, Jun Ye, and P. Zoller. The spelling provided in the manuscript has been retained; please confirm. Although qubit-based quantum computers can potentially tackle this problem more efficiently than classical devices, encoding nonlocal fermionic statistics introduces an overhead in the required resources, limiting their applicability on near-term architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement nonlocal gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydberg-mediated interaction gates, to find efficient circuit decompositions for digital and variational quantum simulation algorithms, illustrated here for molecular energy estimation. Finally, we consider a combined fermion-qubit architecture, where both the motional and internal degrees of freedom of the atoms are harnessed to efficiently implement quantum phase estimation as well as to simulate lattice gauge theory dynamics.
Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics.-5.4pc]Please note that the spelling of the following author names in the manuscript differs from the spelling provided in the article metadata: D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, Jun Ye, and P. Zoller. The spelling provided in the manuscript has been retained; please confirm. Although qubit-based quantum computers can potentially tackle this problem more efficiently than classical devices, encoding nonlocal fermionic statistics introduces an overhead in the required resources, limiting their applicability on near-term architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement nonlocal gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydberg-mediated interaction gates, to find efficient circuit decompositions for digital and variational quantum simulation algorithms, illustrated here for molecular energy estimation. Finally, we consider a combined fermion-qubit architecture, where both the motional and internal degrees of freedom of the atoms are harnessed to efficiently implement quantum phase estimation as well as to simulate lattice gauge theory dynamics.
Many-body fermionic systems can be simulated in a hardware-efficient manner using a fermionic quantum processor. Neutral atoms trapped in optical potentials can realize such processors, where nonlocal fermionic statistics are guaranteed at the hardware level. Implementing quantum error correction in this setup is, however, challenging, due to the atom-number superselection present in atomic systems, that is, the impossibility of creating coherent superpositions of different particle numbers. In this Letter, we overcome this constraint and present a blueprint for an error-corrected fermionic quantum processor that can be implemented using current experimental capabilities. To achieve this, we first consider an ancillary set of fermionic modes and design a fermionic reference, which we then use to construct superpositions of different numbers of referenced fermions. This allows us to build logical fermionic modes that can be error corrected using standard atomic operations. Here, we focus on phase errors, which we expect to be a dominant source of errors in neutral-atom quantum processors. We then construct logical fermionic gates, and show their implementation for the logical particle-number conserving processes relevant for quantum simulation. Finally, our protocol is illustrated with a minimal fermionic circuit, where it leads to a quadratic suppression of the logical error rate.
Quantum simulations of many-body systems are among the most promising applications of quantum computers1. In particular, models based on strongly correlated fermions are central to our understanding of quantum chemistry and materials problems2, and can lead to exotic, topological phases of matter3,4. However, owing to the non-local nature of fermions, such models are challenging to simulate with qubit devices5. Here we realize a digital quantum simulation architecture for two-dimensional fermionic systems based on reconfigurable atom arrays6. We utilize a fermion-to-qubit mapping based on Kitaev’s model on a honeycomb lattice3, in which fermionic statistics are encoded using long-range entangled states7. We prepare these states efficiently using measurement8 and feedforward9, realize subsequent fermionic evolution through Floquet engineering10,11 with tunable entangling gates12 interspersed with atom rearrangement, and improve results with built-in error detection. Leveraging this fermion description of the Kitaev spin model, we efficiently prepare topological states across its complex phase diagram13 and verify the non-Abelian spin-liquid phase3 by evaluating an odd Chern number14,15. We further explore this two-dimensional fermion system by realizing tunable dynamics and directly probing fermion exchange statistics. Finally, we simulate strong interactions and study the dynamics of the Fermi–Hubbard model on a square lattice. These results pave the way for digital quantum simulations of complex fermionic systems for materials science, chemistry16 and high-energy physics17. Digital quantum simulations of Kitaev’s honeycomb model are realized for two-dimensional fermionic systems using a reconfigurable atom-array processor and used to study the Fermi–Hubbard model on a square lattice.
Quantum processors have the potential to significantly advance our understanding of quantum systems. In particular, the programmability of digital quantum devices enables access to highly tunable quantum dynamics and observables. The central challenge, however, is suppressing errors, making quantum error correction essential for large-scale algorithms. In this thesis, I present work on quantum processing with reconfigurable atom arrays, with experiments featuring up to 448 neutral atom qubits, high two-qubit gate fidelities, arbitrary connectivity, and mid-circuit qubit readout and reuse. Using this system, I describe how we realize gate-based quantum simulations. In particular, we experimentally study Kitaev’s honeycomb model and explore hardware-efficient fermion-to-qubit encodings. We then leverage unique opportunities with atoms to study the key building blocks of scalable quantum error correction. These include below-threshold performance, deep computation at constant entropy, and universal logical gates. Together, these experiments highlight unique near-term opportunities with atom arrays and chart a path toward future large-scale atomic processors.
Simulating the real-time dynamics of lattice gauge theories, underlying the Standard Model of particle physics, is a notoriously difficult problem where quantum simulators can provide a practical advantage over classical approaches. In this work, we present a complete Rydberg-based architecture, co-designed to digitally simulate the dynamics of general gauge theories coupled to matter fields in a hardware-efficient manner. Ref. \cite{Gonzalez_2022} showed how a qudit processor, where non-abelian gauge fields are locally encoded and time-evolved, considerably reduces the required simulation resources compared to standard qubit-based quantum computers. Here we integrate the latter with a recently introduced fermionic quantum processor \cite{Gonzalez_2023}, where fermionic statistics are accounted for at the hardware level, allowing us to construct quantum circuits that preserve the locality of the gauge-matter interactions. We exemplify the flexibility of such a fermion-qudit processor by focusing on two paradigmatic high-energy phenomena. First, we present a resource-efficient protocol to simulate the Abelian-Higgs model, where the dynamics of confinement and string breaking can be investigated. Then, we show how to prepare hadrons made up of fermionic matter constituents bound by non-abelian gauge fields, and show how to extract the corresponding hadronic tensor. In both cases, we estimate the required resources, showing how quantum devices can be used to calculate experimentally-relevant quantities in particle physics.
The motion of atoms in programmable optical tweezer arrays offers many new opportunities for neutral atom quantum science. These include inter- and intra-site atom motion for resource-efficient implementations of fermionic and bosonic modes, respectively, as well as tweezer transport for efficient compilation of arbitrary circuits. However, the exploitation of atomic motion for all three purposes and others is limited by the inertia of the atoms. We present a comprehensive architectural blueprint for the use of fermionic metastable helium-3 (3He∗) atoms -- the lightest trappable atomic species -- in programmable optical tweezer arrays. This includes a concrete analysis of atomic structure considerations as well as Rydberg-mediated interactions. We show that inter-tweezer hopping of 3He∗ atoms can be ≳3× faster than previous demonstrations with lithium-6. We also demonstrate a new toolbox for encoding and manipulating qubits directly in the tweezer trap potential, uniquely enabled by the light mass of 3He∗. Finally, we provide several examples of new opportunities for fermionic quantum simulation and computation that leverage the transport and inter-tweezer hopping of 3He∗ atom arrays. These tools present new methods to improve the resource efficiency of neutral atom quantum science that may also enable quantum simulations of lattice gauge theories and quantum chemistry outside the Born-Oppenheimer approximation
Fermionic atoms in optical lattices provide a native implementation of Fermi-Hubbard (FH) models that can be used as analog quantum simulators of many-body fermionic systems. Recent experimental advances include the time-dependent local control of chemical potentials and tunnelings, and thus enable us to operate this platform digitally as a programmable quantum simulator. Here, we explore these opportunities and develop ground-state preparation algorithms for different fermionic models, based on the ability to implement both single-particle and many-body high-fidelity fermionic gates, as provided by the native FH Hamiltonian. In particular, we first design variational precompiled quantum circuits to prepare the ground state of the natively implemented FH model, with significant speedups relative to competing adiabatic protocols. Besides, the versatility of this variational approach enables us to target extended FH models, i.e., including terms that are not natively realized on the platform. As an illustration, we include next-nearest-neighbor tunnelings at finite dopings, relevant in the context of d -wave superconductivity. Furthermore, we discuss how to approximate the imaginary-time evolution using variational fermionic circuits, both as an alternative state-preparation strategy and as a subroutine for the quantum Lanczos algorithm to further improve the energy estimation. We benchmark our protocols for ladder geometries, though they can be readily applied to two-dimensional experimental setups to address regimes beyond the capabilities of current classical methods. These results pave the way for more efficient and comprehensive explorations of relevant many-body phases with existing programmable fermionic quantum simulators.